Number worksheet — GCSE Higher

1.Simplify ⁴√(16a⁸b¹²)

2.n is a whole number and 2 ≤ n < 6. Write down all the possible values of n.

3.Write down the symbol that makes this statement true: −2/3 ___ −5/6

4.A country has an area of 25,000,000 hectares. Write this area in standard form.

5.Simplify x⁽³⁄⁴⁾ ÷ x⁽¹⁄⁴⁾

6.At a bus station one bus leaves every 6 minutes and another leaves every 9 minutes. The two buses leave together at the start of the day. Work out how long it is until they next leave together.

7.Work out ∛(−27) + ∛8

8.4ˣ = 64. Work out the value of x.

9.The highest common factor of two numbers is 4 and their lowest common multiple is 60. One of the numbers is 20. Work out the other number.

10.A rectangular tile measures 45 cm by 0.6 m. Work out its area, in square centimetres.

11.A board game has 5 different character pieces and 4 different colour tokens. The dragon piece can only be used with the gold token. Work out how many different combinations of one character piece and one colour token are possible.

12.The distance from the Earth to the Moon is 384,000 km. Write this distance in standard form, in kilometres.

13.The number of visitors to a museum on Saturday is given as 1,800, correct to the nearest 100. Which of these could not be the actual number of visitors?

14.Write 0.875 as a fraction in its simplest form.

15.Robert is converting 0.999... (with the 9s recurring forever) into a fraction. He lets x = 0.999... . Multiplying by 10 gives 10x = 9.999... . Subtracting x from 10x gives 9x = 9, so x = 1. Which statement correctly explains this result?